LCM of 36, 60 and 72 is 360. LCM of 36, 60, and 72 is the smallest number among all common multiples of 36, 60, and 72. The first few multiples of 36, 60, and 72 are (36, 72, 108, 144, 180 . . .), (60, 120, 180, 240, 300 . . .), and (72, 144, 216, 288, 360 . . .) respectively. There are 3 commonly used methods to find LCM of 36, 60, 72 – by prime factorization, by division method, and by listing multiples. In Maths, the LCM of any two numbers is the value which is evenly divisible by the given two numbers.
Also read: Least common multiple
What is LCM of 36, 60 and 72?
The answer to this question is 360. The LCM of 36, 60 and 72 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 36, 60 and 72, is the smallest positive integer 360 which is divisible by both 36, 60 and 72 with no remainder.
How to Find LCM of 36, 60 and 72?
LCM of 36, 60 and 72 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 36, 60 and 72 Using Prime Factorisation Method
The prime factorisation of 36, 60 and 72, respectively, is given by:
36 = (2 × 2 × 3 × 3) = 22 × 32,
60 = (2 × 2 × 3 × 5) = 22 × 31 × 51, and
72 = (2 × 2 × 2 × 3 × 3) = 23 × 32
LCM (36, 60, 72) = 360
LCM of 36, 60 and 72 Using Division Method
We’ll divide the numbers (36, 60, 72) by their prime factors to get the LCM of 36, 60 and 72 using the division method (preferably common). The LCM of 36, 60 and 72 is calculated by multiplying these divisors.
| 2 | 36 | 60 | 72 |
| 2 | 18 | 30 | 36 |
| 2 | 9 | 15 | 18 |
| 3 | 9 | 15 | 9 |
| 3 | 3 | 5 | 3 |
| 5 | 1 | 5 | 1 |
| x | 1 | 1 | 1 |
No further division can be done.
Hence, LCM (36, 60, 72) = 360
LCM of 36, 60 and 72 Using Listing the Multiples
To calculate the LCM of 36, 60 and 72 by listing out the common multiples, list the multiples as shown below.
| Multiples of 36 | Multiples of 60 | Multiples of 72 |
| 36 | 60 | 72 |
| 72 | 120 | 144 |
| 108 | 180 | 216 |
| 144 | 240 | 288 |
| …. | 300 | 360 |
| 360 | 360 | 432 |
The smallest common multiple of 36, 60 and 72 is 360.
Therefore LCM (36, 60, 72) = 360
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LCM of 36, 60 and 72 Solved Example
Find the smallest number that is divisible by 36, 60, 72 exactly.
Solution:
The smallest number that is divisible by 36, 60, and 72 exactly is their LCM.
Multiples of 36, 60, and 72:
Multiples of 36 = 36, 72, 108, 144, 180, 216, 252, 288, 324, 360, . . . .
Multiples of 60 = 60, 120, 180, 240, 300, 360, . . . .
Multiples of 72 = 72, 144, 216, 288, 360, . . . .
Therefore, the LCM of 36, 60, and 72 is 360.
Frequently Asked Questions on LCM of 36, 60 and 72
What is the LCM of 36, 60 and 72?
List the methods used to find the LCM of 36, 60 and 72.
What is the Least Perfect Square Divisible by 36, 60, and 72?
LCM of 36, 60, and 72 = 2 × 2 × 2 × 3 × 3 × 5 [Incomplete pair(s): 2, 5] ⇒ Least perfect square divisible by each 36, 60, and 72 = LCM(36, 60, 72) × 2 × 5 = 3600 [Square root of 3600 = √3600 = ±60] Therefore, 3600 is the required number.
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